We consider a heterogeneous two-server system processing fixed size jobs. This includes the scheduling system, where jobs wait in a common queue, and the dispatching system, where jobs are assigned to server-specific queues upon arrival. The optimal policy with respect to the delay in both systems is a threshold policy characterized by a single parameter. In this special case, the scheduling an...

We examine the problem of how best to route jobs among two queues whose servers are subject to breakdowns and repairs. The optimal routing policy is computed by modelling the system as a discrete-time, finite-state Markov decision process and solving the resulting dynamic programming equations either iteratively or by applying the ‘policy improvement’ algorithm. In a series of numerical experim...

The cμ rule is known to be optimal in many queueing systems with memoryless service and inter-arrival times. We establish a cμ rule for a parallel flexible server system with two tiers. Multiple job classes arrive and wait in separate queues. The first tier contains classes that can only be served by one server each, and the second tier contains a class that can be served by all servers. The cμ...